Requesting a recommendation letter to professor to transfer to university

Hi guys! Please leave me some comments or correction!! Thanks in advance!! :):)

Dear Professor XXXXXXX,

My name is XXXXXX, I was in your ******* class on 2013 in third year of (name of course), and am currently on gap year due to military service in Korea.

Since I finished army service last June, I am planning to transfer to (Name of university) for upcoming semester on next year. However, in order to transfer to (Name of university), the recommendation letter is necessarily required.

Therefore, I am writing to ask about if it is possible to ask write me a letter of recommendation letter for transfer to (Name of university).

I know you are extremely busy, so I would be really honored if you were able to write me the letter.
I thank you so much for your time and consideration.

Yours sincerely,

(full name)

You should probably include what you want to study so that the professor can have a better idea of what he should say.